[YesMehFriend]

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You need to either fold this on the flop or call him down. I dont understand what your thinking ifolding to a K on the turn, what exactly does that change? I mean AT is a likely holding, K is just a blank.

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I didn't say we have to fold when a K hits I said: "I guess we should check and reevaluate based on board texture + villains action. "
I'm more likely to call down / c/r on a Q/K turn than on an A.
My line was calling the flop and then reevaluating the turn when a A/K/Q/T hits - this doesn't always mean fold - but when villain pushes the rest of his stack into the 24$ pot after the K hit, I doubt that calling would be correct there.
Besides that we can't fully rule out KT imo, it's not too likely but neither is it impossible.

And for the river: do we really c/c there after c/c the turn? I mean will villain bet a weaker hand / bluff again after getting called twice? He needs to hold almost exactly AT for that or maybe I'm just wrong ...